Hamiltonian structure of bi-gravity, problem of ghost and bifurcation

TL;DR

This paper investigates the Hamiltonian structure of bi-gravity theories with specific interaction terms, identifying conditions for ghost freedom and analyzing the constraints that prevent ghost instabilities, especially near bifurcation points.

Contribution

It provides a detailed Hamiltonian analysis of bi-gravity with scalar interaction functions, clarifying the conditions for ghost-free formulations and the nature of constraints at bifurcation points.

Findings

Necessary conditions for ghost-free interaction terms.

Constraint analysis of Hassan-Rosen bi-gravity.

Identification of bifurcation points affecting ghost constraints.

Abstract

We analyze the Hamiltonian structure of a general theory of bi-gravity where the interaction term is a scalar function of the form $ V(\mathcal{X}^{n}) $ where $ \mathcal{X} $ may be $\sqrt{g^{-1}f} $ or $ g^{-1}f $. We give necessary conditions for the interaction term of such a theory to be ghost free. We give a precise constraint analysis of the bi-gravity theory of Hassan- Rosen and show that the additional constraint which omit the ghost is just one possibility at the bifurcation point.